This article establishes a connection between twin level and component level models of magnetic shape memory alloys (MSMA). Their magneto-mechanical behavior is characterized by the reorientation of martensitic variants along twin boundaries to minimize the energy with respect to the applied mechanical and magnetic loads. This reorientation is impaired by the dissipative nature of the so-called twinning stress, which results in a hysteretic behavior. For individual twin domains, the hysteresis can be directly described using meaningful inequalities. On component level, phenomenological hysteresis models are typically used, which can be more easily integrated in control schemes. This paper shows the conversion of the twinning stress distribution on twin level into the Everett-function for a generic Preisach-type phenomenological model describing the component level and vice versa. The proposed bidirectional approach bridges the different model scales for mechanical and magnetic loads by combining their corresponding parameters. The parameter conversion is validated using a numerical model on twin level that fully implements the switching domains.